// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include <Eigen/Dense>

#define NUMBER_DIRECTIONS 16
#include <unsupported/Eigen/AdolcForward>

template<typename Vector>
EIGEN_DONT_INLINE typename Vector::Scalar
foo(const Vector& p)
{
	typedef typename Vector::Scalar Scalar;
	return (p - Vector(Scalar(-1), Scalar(1.))).norm() + (p.array().sqrt().abs() * p.array().sin()).sum() + p.dot(p);
}

template<typename _Scalar, int NX = Dynamic, int NY = Dynamic>
struct TestFunc1
{
	typedef _Scalar Scalar;
	enum
	{
		InputsAtCompileTime = NX,
		ValuesAtCompileTime = NY
	};
	typedef Matrix<Scalar, InputsAtCompileTime, 1> InputType;
	typedef Matrix<Scalar, ValuesAtCompileTime, 1> ValueType;
	typedef Matrix<Scalar, ValuesAtCompileTime, InputsAtCompileTime> JacobianType;

	int m_inputs, m_values;

	TestFunc1()
		: m_inputs(InputsAtCompileTime)
		, m_values(ValuesAtCompileTime)
	{
	}
	TestFunc1(int inputs_, int values_)
		: m_inputs(inputs_)
		, m_values(values_)
	{
	}

	int inputs() const { return m_inputs; }
	int values() const { return m_values; }

	template<typename T>
	void operator()(const Matrix<T, InputsAtCompileTime, 1>& x, Matrix<T, ValuesAtCompileTime, 1>* _v) const
	{
		Matrix<T, ValuesAtCompileTime, 1>& v = *_v;

		v[0] = 2 * x[0] * x[0] + x[0] * x[1];
		v[1] = 3 * x[1] * x[0] + 0.5 * x[1] * x[1];
		if (inputs() > 2) {
			v[0] += 0.5 * x[2];
			v[1] += x[2];
		}
		if (values() > 2) {
			v[2] = 3 * x[1] * x[0] * x[0];
		}
		if (inputs() > 2 && values() > 2)
			v[2] *= x[2];
	}

	void operator()(const InputType& x, ValueType* v, JacobianType* _j) const
	{
		(*this)(x, v);

		if (_j) {
			JacobianType& j = *_j;

			j(0, 0) = 4 * x[0] + x[1];
			j(1, 0) = 3 * x[1];

			j(0, 1) = x[0];
			j(1, 1) = 3 * x[0] + 2 * 0.5 * x[1];

			if (inputs() > 2) {
				j(0, 2) = 0.5;
				j(1, 2) = 1;
			}
			if (values() > 2) {
				j(2, 0) = 3 * x[1] * 2 * x[0];
				j(2, 1) = 3 * x[0] * x[0];
			}
			if (inputs() > 2 && values() > 2) {
				j(2, 0) *= x[2];
				j(2, 1) *= x[2];

				j(2, 2) = 3 * x[1] * x[0] * x[0];
				j(2, 2) = 3 * x[1] * x[0] * x[0];
			}
		}
	}
};

template<typename Func>
void
adolc_forward_jacobian(const Func& f)
{
	typename Func::InputType x = Func::InputType::Random(f.inputs());
	typename Func::ValueType y(f.values()), yref(f.values());
	typename Func::JacobianType j(f.values(), f.inputs()), jref(f.values(), f.inputs());

	jref.setZero();
	yref.setZero();
	f(x, &yref, &jref);
	//     std::cerr << y.transpose() << "\n\n";;
	//     std::cerr << j << "\n\n";;

	j.setZero();
	y.setZero();
	AdolcForwardJacobian<Func> autoj(f);
	autoj(x, &y, &j);
	//     std::cerr << y.transpose() << "\n\n";;
	//     std::cerr << j << "\n\n";;

	VERIFY_IS_APPROX(y, yref);
	VERIFY_IS_APPROX(j, jref);
}

EIGEN_DECLARE_TEST(forward_adolc)
{
	adtl::setNumDir(NUMBER_DIRECTIONS);

	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST((adolc_forward_jacobian(TestFunc1<double, 2, 2>())));
		CALL_SUBTEST((adolc_forward_jacobian(TestFunc1<double, 2, 3>())));
		CALL_SUBTEST((adolc_forward_jacobian(TestFunc1<double, 3, 2>())));
		CALL_SUBTEST((adolc_forward_jacobian(TestFunc1<double, 3, 3>())));
		CALL_SUBTEST((adolc_forward_jacobian(TestFunc1<double>(3, 3))));
	}

	{
		// simple instantiation tests
		Matrix<adtl::adouble, 2, 1> x;
		foo(x);
		Matrix<adtl::adouble, Dynamic, Dynamic> A(4, 4);
		;
		A.selfadjointView<Lower>().eigenvalues();
	}
}
